Time Dependent Differential Yield as a Scale-up Parameter in Enzyme and Fermentation Reactors

Area of Science:

• Biochemical Engineering
• Enzyme Kinetics
• Bioprocess Modeling

Background:

• Enzyme-substrate kinetics are fundamental to understanding biological and industrial processes.
• Yield functions are critical for quantifying the efficiency of enzyme and fermentation systems.
• Existing models often simplify the complex relationship between enzyme concentration and substrate availability.

Purpose of the Study:

• To investigate the differential yield function in enzyme-substrate kinetic models.
• To analyze the asymptotic behavior of the yield function as substrate concentration approaches zero.
• To explore the relationship between the differential yield function and commonly used yield constants.

Main Methods:

• Mathematical analysis of the yield function under pseudo-steady-state conditions.
• Application of Michaelis-Menten and Briggs-Haldane kinetics to bound the differential yield function.
• Investigation of the dimensionless parameter epsilon (k(m)/E*)'s role in asymptotic yield.
• Demonstration of mathematical results using experimental data from horseradish peroxidase and gluconic acid fermentation.

Main Results:

• The differential yield function is bounded by yield functions derived from Michaelis-Menten and Briggs-Haldane models.
• The common yield constant is an integral average of the differential yield function.
• The average yield constant provides a method for assessing data consistency.
• The parameter epsilon influences the asymptotic yield.

Conclusions:

• The study provides a rigorous mathematical framework for understanding enzyme yield functions.
• The findings enhance the interpretation and consistency analysis of data from enzyme and fermentation systems.
• The research offers improved methods for modeling and optimizing bioprocesses.